The equation of a circle $C$ is $x^2+y^2+6x+2y-26 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2+6x) + (y^2+2y) = 26$ $(x^2+6x+9) + (y^2+2y+1) = 26 + 9 + 1$ $(x+3)^{2} + (y+1)^{2} = 36 = 6^2$ Thus, $(h, k) = (-3, -1)$ and $r = 6$.